[97-98] Psychology shows, for its part, that all our sensations (these immediate and ultimate data of experience) possess one property: extensiveness or extension...

Geometric space is the result of an abstract interpretation of optical space,—an interpretation that strips away individual properties, generalizes, and makes more accessible to the mind the relations contained in this optical space. We would willingly supplement Mach's thought with the assertion that the goal of this operation is to give these relations the most rigorous and precise, universal and necessary, and consequently objective expression...

[100] Thus, mathematics reveals to us the relations between things from the point of view of order, number, and extension.

By analyzing the real relations existing between things, our mind naturally acquires the ability to form analogous relations through association by similarity. It can therefore devise such combinations as do not occur in reality, proceeding from those which do occur in it. Having first formed representations that are copies of the real, we can then form such as are models, as Taine says in a somewhat different sense.

NB
sensation
= ultimate
Mach + objectivity
!!!
484
V. I. LENIN